Question

The given graph is discontinuous at $x=a$ because the limit doesn't exist at $x=a$

• A. True
• B. False

Answer 1

The correct option is A

True

This is one way of having discontinuity. i.e., to have a sudden break of graph at a point and the following curve starts at some other point. This is the case where left hand and right hand limits are different from each other.

i.e., Here,

L.H.L $\ne$ R.H.L

or
$\underset{x\to a^{-}}{lim}f\left(x\right)\ne \underset{x\to a^{+}}{lim}f\left(x\right)$
Hence , the given function is discontinuous